Nonperturbative contributions to a resummed leptonic angular distribution in inclusive neutral vector boson production

We present an analysis of nonperturbative contributions to the transverse momentum distribution of $Z/{\gamma }^{*}$ bosons produced at hadron colliders. The new data on the angular distribution ${\varphi }_{\eta }^{*}$ of Drell-Yan pairs measured at the Tevatron are shown to be in excellent agreement with a perturbative QCD prediction based on the Collins-Soper-Sterman (CSS) resummation formalism at next-to-next-to-leading logarithmic (NNLL) accuracy. Using these data, we determine the nonperturbative component of the CSS resummed cross section and estimate its dependence on arbitrary resummation scales and other factors. With the scale dependence included at the NNLL level, a significant nonperturbative component is needed to describe the angular data.

Figure 1

Dependence of $Z$ boson $Q_T$ distribution on the scale parameter $C_2$ at $\mathcal{O}({\alpha }_s^2)$ and $\mathcal{O}({\alpha }_s)$.

Figure 2

The ratios to the central theoretical prediction of the D0 electron data at $|y_Z|\le 1$ and alternative theoretical predictions. The central prediction is computed assuming $C_1=C_3=2b_0$, $C_2=1/2$, $a_Z=1.1{\mathrm{GeV}}^2$, and kinematical correction 1. Theory predictions based on alternative kinematical corrections (0 and 2) and BLNY nonperturbative parametrization are also shown.

Figure 3

Electrons: Scale variation due to $C_{1,2,3}$ at small ${\varphi }_{\eta }^{*}$.

Figure 4

Same as above but for the muons.

Figure 5

Dependence on the nonperturbative parameter $a_Z$ for electrons with $|y_Z|\le 1$.

Figure 6

${\chi }^2/N_{pt}$ as a function of $a_Z$ with fixed $C_{1,2,3}$.

Figure 7

${\chi }^2/N_{pt}$ and scale parameters as a function of $a_Z$ for ${\overline{C}}_1={\overline{C}}_3=2b_0,{\overline{C}}_2=1/2$. The scale parameters are shared across three $y_Z$ bins.

Figure 8

${\chi }^2/N_{pt}$ as a function of $a_Z$ for ${\overline{C}}_1={\overline{C}}_3=2b_0,{\overline{C}}_2=1/2$. The scale parameters are independent in each $y_Z$ bin.

Figure 9

The 68% C.L. ranges for $a_Z$ in individual $y_Z$ bins and in all bins.

Figure 10

Data vs theory ratios for the $Q_T$ distribution by ATLAS 7 TeV, $35–40{\text{pb}}^{-1}$ [26] and ${\varphi }_{\eta }^{*}$ distribution ATLAS 7 TeV, $4.6{\text{fb}}^{-1}$ [27].